Euphemisms are figures of speech used in place of more offensive terms. In this comic, Cueball uses swear words in the place of benign terms, inverting the typical usage of euphemisms. To "drop the kids off at the pool" is a euphemism meaning to "go take a shit." In this case, however, Cueball actually has to drop kids off at the pool but instead uses "go take a shit." Cueball is using the euphemism in reverse, hence the title.

In the title text, the figure is waiting for a situation in which he has to see a man concerning a horse, as this relates to another euphemism meaning to urinate. It can be assumed that, when telling someone about seeing the man about the horse, he would say "...then I had to go take a piss."

This is not to be confused with the opposite of a euphemism called a dysphemism.

Why is this not a good example of a reverse euphemism? His kids are shit. The toilet bowl is basically a pool for shit. "Take a shit" translates directly to "Drop kids off at the pool".
In a true euphemism, "pass away" translates directly to "died".
The two seem similar.

One day I want to be able to really confuse someone by saying "we had to buy some more paint the other day because my dad died" 108.162.223.221 14:48, 28 January 2016 (UTC)Dream

I am unfamiliar with "seeing a man about a horse" meaning "taking a piss". Is there any reason why man and horse are related to urination? 162.158.34.137 16:30, 6 May 2016 (UTC)

"Going to see a man about {something / an animal}" is a way of giving a reason for your absence, rather than announcing an intent to perform a bodily function, or simply a polite way of saying "Where I'm going is none of your business". 141.101.98.69 22:01, 30 May 2016 (UTC)

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